A new approach is presented for the safety analysis of structures subjected to bounded but uncertain mechanical parameters of rock material based on convex model theory. An optimization solution of the approach is adopted. First

it defines the uncertain material parameters with a convex model when the amount of information available on the uncertain material parameters is not enough to accurately define. The worst cases are searched over this convex model by using the optimization methods. The safety parameters’ domain of rock material is then got. The approach is reasonable; and the whole process is feasible.